Design of a global extremum seeking algorithm for an omni-directional robot model

Abstract

A global extremum seeking algorithm is developed for a mobile robot model where the aim is to find the location of the most powerful signal source among the others. In other words, the control problem is to seek the global extremum point of a performance function when there are local extremas. The locations of the signal sources and signal distribution characteristics are unknown, i.e. the gradient of the performance function is unknown. The control algorithm also doesn't use any position measurement of the mobile robot itself. Henceforth, the controller is suitable for the missions where the robot moves in an unknown terrain with no GPS signal and no inertial measurements. Only the signal magnitude should be measured via a sensor mounted on the robot during the motion. A gradient estimator is designed to determine the motion direction towards the extremum point. When a local extremum is found, the robot will continue its search for another extremum points. Once each extremums have been visited, the robot will compare the signal levels on each source and identify the global extremum i.e. the most powerful signal source. In the absence of any position measurements, the robot can move towards the global extremum by repeating its motion history backwards. In the literature, this is the first global extremum seeking algorithm that has been developed for an omni-directional mobile robot model. Via the simulation studies it has been shown that the control algorithm can seek and find both stationary and non stationary signal sources and it can find the global extremum point when there are local extremas.